Description

Book Synopsis
This concise introduction covers all of the measure theory and probability most useful for statisticians. Originating from the authors' own graduate course, it is perfect for a two-term course or for self-study. It is especially useful to graduate students in related fields who want to shore up their mathematical foundation.

Table of Contents
Preface; Acknowledgements; 1. Point sets and certain classes of sets; 2. Measures: general properties and extension; 3. Measurable functions and transformations; 4. The integral; 5. Absolute continuity and related topics; 6. Convergence of measurable functions, Lp-spaces; 7. Product spaces; 8. Integrating complex functions, Fourier theory and related topics; 9. Foundations of probability; 10. Independence; 11. Convergence and related topics; 12. Characteristic functions and central limit theorems; 13. Conditioning; 14. Martingales; 15. Basic structure of stochastic processes; References; Index.

A Basic Course in Measure and Probability Theory For Applications

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    A Paperback by Ross Leadbetter, Stamatis Cambanis, Vladas Pipiras

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      Publisher: Cambridge University Press
      Publication Date: 30/01/2014
      ISBN13: 9781107652521, 978-1107652521
      ISBN10:
      Also in:
      Mathematics Calculus and mathematical analysis Probability and statistics

      Description

      Book Synopsis
      This concise introduction covers all of the measure theory and probability most useful for statisticians. Originating from the authors' own graduate course, it is perfect for a two-term course or for self-study. It is especially useful to graduate students in related fields who want to shore up their mathematical foundation.

      Table of Contents
      Preface; Acknowledgements; 1. Point sets and certain classes of sets; 2. Measures: general properties and extension; 3. Measurable functions and transformations; 4. The integral; 5. Absolute continuity and related topics; 6. Convergence of measurable functions, Lp-spaces; 7. Product spaces; 8. Integrating complex functions, Fourier theory and related topics; 9. Foundations of probability; 10. Independence; 11. Convergence and related topics; 12. Characteristic functions and central limit theorems; 13. Conditioning; 14. Martingales; 15. Basic structure of stochastic processes; References; Index.

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